I just got back from the Whites last night. I started my hike on Thursday afternoon from Schulman Grove and was going to do a 50 mile loop that would have taken me up to Barcroft. Unfortunately, I took a really bad tumble yesterday morning trying to get around a stream crossing in Wyman Canyon and had to hike out. I badly tore up my thumb and ear, got a big bump on my head, and have a mildly injured knee. I was really bummed to have to end the trip early but things could have been much worse.
In regards to snow. The road is open to Schulman Grove but is closed beyond that. There is patchy snow in the Schulman Grove (10,000 ft) to one mile north. Once I started dropping down toward Wyman Canyon the snow disappeared. The road north of Schulman (which is closed) is plowed but muddy. Last week the White Mountain Research Station snowcat was plowing it to get to Crooked Creek Station which I suspect will open by June 10 or 15, if not before. Barcroft Station probably won't open until July 1 at the earliest. Once the road up to the gate opens it will probably be really muddy in spots. For more info and snow pictures check out:
Hope this helps.
Below are some pictures from my trip. Sorry to hijack this thread to post my trip report.
Looking toward Barcoft and the Pelissier Flats from WMRS Owens Valley Lab
Looking toward the Sierra from Schulman Grove
Mileages from Schulman Grove
White Mountain Road north of Schulman Grove
Dropping out of Coldwater Spring Meadow (10,000 ft)
Abandoned rancher shack in Wyman Canyon
South side of Blanco Mountain